A new mechanism of current driven by a wave is discussed. There is a series of resonant regions in the velocity space of a magnetized plasma interacting with a single wave. When the amplitude of the wave is higher than a threshold, some of the resonant regions will overlap each other and the stochastic effect will appear. If the overlapping region is asymmetric in the longtudinal velocity distribution of the electrons, the plasma current may be driven by the wave as a result of the stochastic effect.